Subgroups — C₃×#135 #975

Order 96.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#41	C₂	1	2	yes	maximal, complemented
2	C₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×SD₁₆	C₂	1	2	yes	maximal, complemented
4	C₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#135	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₃×Q₈	C₂²	1	2	yes	—
8	C₃×D₄	—	2	2	no	—
9	C₃×D₄	C₂²	1	2	yes	—
10	C₂×C₃×C₄	—	2	2	no	—
11	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
12	C₃×C₈	C₂²	1	1	yes	characteristic
13	C₃×C₈	C₂²	1	1	yes	characteristic
14	#41	C₂×C₃	1	2	yes	complemented
15	Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
16	SD₁₆	C₂×C₃	1	2	yes	complemented
17	D₈	C₂×C₃	1	1	yes	characteristic, complemented
18	C₂×C₈	C₂×C₃	1	1	yes	characteristic, complemented
19	C₂²×C₃	—	2	2	no	—
20	C₂²×C₃	D₄	1	1	yes	characteristic
21	C₃×C₄	—	2	2	no	—
22	C₃×C₄	D₄	1	1	yes	characteristic
23	C₃×C₄	C₂³	1	1	yes	characteristic
24	Q₈	C₂²×C₃	1	2	yes	—
25	D₄	—	2	2	no	—
26	D₄	C₂²×C₃	1	2	yes	—
27	C₂×C₄	—	2	2	no	—
28	C₂×C₄	C₂²×C₃	1	1	yes	characteristic
29	C₈	C₂²×C₃	1	1	yes	characteristic
30	C₈	C₂²×C₃	1	1	yes	characteristic
31	C₂×C₃	—	2	1	no	—
32	C₂×C₃	—	4	2	no	—
33	C₂×C₃	C₂×D₄	1	1	yes	characteristic
34	C₂²	—	2	2	no	—
35	C₂²	C₃×D₄	1	1	yes	characteristic
36	C₄	—	2	2	no	—
37	C₄	C₃×D₄	1	1	yes	characteristic
38	C₄	C₂³×C₃	1	1	yes	characteristic
39	C₃	#135	1	1	yes	characteristic, direct product factor, Sylow
40	C₂	—	2	1	no	—
41	C₂	—	4	2	no	—
42	C₂	C₂×C₃×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	D₄
commutator, Frattini, cosocle	C₄	C₂³×C₃
socle	C₂×C₃	C₂×D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃×C₄ ◁ C₂×C₃×C₄ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃×#41	C₂	semidirect
2. C₃×Q₁₆	C₂	semidirect
3. C₃×SD₁₆	C₂	semidirect
4. C₃×D₈	C₂	semidirect
5. C₂×C₃×C₈	C₂	semidirect
6. #135	C₃	direct (N × H)
14. #41	C₂×C₃	semidirect
15. Q₁₆	C₂×C₃	semidirect
16. SD₁₆	C₂×C₃	semidirect
17. D₈	C₂×C₃	semidirect
18. C₂×C₈	C₂×C₃	semidirect
39. C₃	#135	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×#41	2
C₃×Q₁₆	2
C₃×SD₁₆	2
C₃×D₈	2
C₂×C₃×C₈	2
#135	3

Subgroups — C3×#135 #975

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#135 #975